This invention is related to subsurface modeling, and is more particularly concerned with a parametric subsurface modeling method, apparatus, and article of manufacture that use uncertainty estimates of subsurface model parameters.
Subsurface models are typically created by geoscientists and engineers to allow development strategies for the subsurface area to be evaluated. Models of this type are commonly created in connection with the development of hydrocarbon reservoirs and mining sites, but they can also used during drilling and related activities where the physical properties of the subsurface area are important. This patent application will focus on the process of creating and updating a model of a subsurface hydrocarbon reservoir, but it should be understood that this merely represents one specific example of how a model of any subsurface area may be created and updated.
Currently, hydrocarbon reservoir modeling is performed most commonly in high-risk, high-profile situations. Typical applications include discoveries in new areas, deepwater exploration, fields in which production surprises or drilling hazards have been encountered, fields in which secondary and tertiary recovery activities are planned, and fields which are being considered for sale or abandonment. The failure to adequately model hydrocarbon reservoirs can have numerous adverse financial consequences, including inaccurate reserve calculations, drilling or completion problems, improper production facility sizing, and suboptimal well placement.
The general problem addressed by this invention is how to construct a model of a subsurface area that is in agreement with multiple sets of measurement data. A model that is in agreement with all of the measurement data obtained from the reservoir can help address many of the problems noted above. By xe2x80x98reservoir modelxe2x80x99 we mean a quantitative parameterized representation of the subsurface in terms of geometries and material properties. The geometrical model parameters will typically identify geological boundaries, such as contacts between different geologic layers, faults, or fluid/fluid interfaces. The material model parameters will typically identify properties of distributed subsurface materials, such as seismic wave velocities, porosities, permeabilities, fluid saturations, densities, fluid pressures, or temperatures.
By xe2x80x98agreementxe2x80x99 we mean that the data predicted from the reservoir model fit measurements made on the actual reservoir (seismic data, drilling data, well logging data, well test data, production history data, permanent monitoring data, ground penetrating radar data, gravity measurements, etc.). Virtually all types of measurement data have quantifiable uncertainties and the reservoir model agrees with the measurement data when the difference between data predicted by the reservoir model and measurement data obtained from the reservoir is less than this inherent measurement uncertainty. While creating a reservoir model that fits one data set is a relatively straightforward task, it is much more difficult to ensure that the model is in agreement with multiple data sets, particularly if the data sets consist of different types of data.
A reservoir model, however, is nonunique even if it is made to fit a variety of data, because different values of material properties and geometries within the model can result in similar predicted measurement values. In other words, the reservoir model has inherent uncertainties: each of the numerical parameters in the reservoir model (e.g., values of material properties within a layer) can take a range of values while the model remains in agreement with the data. This range in parameter values is the uncertainty associated with the reservoir model. The invention described herein is a method to integrate information from multiple measurements and to obtain a reservoir model with quantitative uncertainties in the model parameters. A model of the reservoir that fits the data and has quantified uncertainties can be used to assess the risk inherent in reservoir development decisions (e.g., deciding on the location of additional wells) and to demonstrate the value of additional measurements by showing how these measurements decrease uncertainties in model parameters of interest (e.g., the location of a drilling target or hazard).
A Shared Earth Model (SEM) is a geometrical and material property model of a subsurface area. The model is shared, in the sense that it integrates the work of several experts (geologists, geophysicists, well log analysts, reservoir engineers, etc.) who use information from a variety of measurements and interact with the model through different application programs. Ideally, the SEM contains all available information about a reservoir and thus is the basis to make forecasts and plan future actions.
Yet, in any practical case, the information in the measurements is not sufficient to uniquely constrain the parameters (geometries. and material properties) of a SEM. As noted above, any SEM has an associated uncertainty, defined here as the range that model parameters can take while fitting available measurements.
The invention has two primary aspects. The first aspect is a method to quantify and update model parameter uncertainties based on available measurements. One embodiment of this method is based on Bayes"" rule, with SEM uncertainty quantified by a posterior probability density function (PDF) of the model parameters, conditioned on the measurements used to constrain the model. This posterior PDF may be approximated by a multivariate normal distribution, which is fully described by the posterior mean and covariance matrix of the SEM parameters. Alternatively, one can use a Monte Carlo method to obtain a sample of models drawn from the posterior PDF. This sample of models spans the uncertainty implied by the measurements.
The second aspect is how such a measure of uncertainty acts as a xe2x80x98memoryxe2x80x99 of the SEM and can be used for consistent model updating. Quantified uncertainties provide a mechanism to ensure that updates of the SEM based on new data (e.g., well data) are consistent with information provided by data examined previously (e.g., surface seismic data). In particular, we show through a simple example how the effects of a local update of the model can be propagated using the posterior covariance matrix of the SEM parameters. We also show how to update a sample of models obtained by the Monte Carlo method to include new information.
The ideal of a SEM is that all specialists should be able to interact with a common geometry and material property model of the reservoir, incorporating changes into the model using measurements from their own domain of expertise, while maintaining model consistency with previous measurements. This SEM representation would always be consistent with all available information and should be easy to update as soon as new measurements become available (e.g., from additional wells). Model building would not be a task done episodically, but instead the reservoir model would evolve incrementally as more and more information becomes available during development and production.
While acquiring more measurements can reduce uncertainty, it is important to weigh the cost of data acquisition against the benefits of reducing uncertainty. This can be done using the tools of decision theory, where different decisions are compared given their associated gains/costs and current uncertainties. A consistent quantification of uncertainties can assist oil companies in making data acquisition, drilling, or development decisions.
Currently, reservoir models are simply modified to fit new data and confirming that the modification is not inconsistent with the previously obtained measurement data is left up to the discretion of the user. The reservoir model may be the result of years of effort and may incorporate measurement data from a wide variety of sources. A user will often only confirm that the change made is not inconsistent with the measurement data within his or her area of expertise (a well log analyst may confirm, for instance, that the change made is consistent with the other well logging data, but may not determine whether the change has introduced an inconsistency with the seismic or geologic data from the area). Many reservoir simulations rely heavily on production data from wells and only four types of geological or geophysical reservoir information: structure of the top of the reservoir, reservoir thickness, porosity, and the ratio of net pay to gross pay. These maps are often constructed from seismic and well log data alone. Incorporating all available data, such as core analyses, seismic-guided reservoir property distributions and fluid analyses, and making certain that the reservoir model is consistent with these different types of data is a cost-effective way to stregthen and validate reservoir models across disciplines.
An iterative method to obtain a model that fits some of the data has been described by George W. Celniker in commonly-assigned U.S. Pat. No. 5,905,657, issued Mar. 18, 1999 and incorporated herein by reference. In the Celniker method, the user examines the difference between predicted and measured data, modifies the model attempting to decrease this difference, and repeats the procedure until the fit is satisfactory. This procedure may be adequate if all data sets are considered simultaneously, which may be impractical for diverse and large data sets. If instead the model is modified to fit each of the N data sets in turn (say, from d(1) to d(N), there is no guarantee that the modifications made to fit the ith data set d(i) do not make the model inconsistent with any of the data sets examined previously (d(1), d(2), . . . , d(ixe2x88x921). The model can be assured to be consistent with all data sets only by repeating the comparisons with each data set. Also, if a new data set is acquired and the model is modified to fit it, all other data sets must be examined again to ensure consistency. These repeated checks can make the method time-consuming and inefficient in practice. Moreover, an iterative comparison of predicted and measured data does not by itself quantify the uncertainty in the model (defined, e.g., as the range that the model parameters can span while still fitting the measured data).
The invention comprises a parametric subsurface modeling method, apparatus, and article of manufacture that use measurement data to create a model of a subsurface area. The method includes the steps of: creating a parameterized model having an initial estimate of model parameter uncertainties; considering measurement data from the subsurface area; updating the model to fit the measurement data, the updated model having an updated estimate of model parameter uncertainties; and repeating the considering and updating steps with additional measurement data. A computer-based apparatus and article of manufacture for implementing the method are also disclosed. The method, apparatus, and article of manufacture are particularly useful in assisting oil companies in making hydrocarbon reservoir data acquisition and field development decisions. Features of the invention, preferred embodiments and variants thereof, possible applications and their advantages will become appreciated and understood by those skilled in the art from the following detailed description and drawings.